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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd"> <html> <head> <title>page_219</title> <link rel="stylesheet" href="reset.css" type="text/css" media="all"> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /> </head> <body> <table summary="top nav" border="0" width="100%"> <tr> <td align="left" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_218.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_219</strong></td> <td align="right" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_220.html">next page ></a></td> </tr> <tr> <td id="ebook_page" align="left" colspan="3" style="background: #ffffff; padding: 20px;"> <table border="0" width="100%" cellpadding="0"><tr><td align="center"> <table border="0" cellpadding="2" cellspacing="0" width="100%"><tr><td align="left"></td> <td align="right"></td> </tr></table></td></tr><tr><td align="left"><p></p><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="right"><font face="Times New Roman, Times, Serif" size="2" color="#FF0000">Page 219</font></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">the partial derivative with respect to x</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>kg</i></sub></font><font face="Times New Roman, Times, Serif" size="3"> is</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3"><img src="933145365df36d7397e03c07905fc436.gif" border="0" alt="0219-01.GIF" width="375" height="61" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">where</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3"><img src="d9ca37eb072c448ffff04a036dbed5b3.gif" border="0" alt="0219-02.GIF" width="376" height="21" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">and Z</font><font face="Times New Roman, Times, Serif" size="1"><sub>9</sub></font><font face="Times New Roman, Times, Serif" size="3"> is a 1 脳 9 vector of zeros. Typically x</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>ka</i></sub></font><font face="Times New Roman, Times, Serif" size="3"> is modeled as a vector of random biases [i.e., <img src="6311abf0c83d4050c7d0dc60e026a2c2.gif" border="0" alt="C0219-01.GIF" width="47" height="17" /> with <img src="9acde1bc7099cdd2950eb69d54dbc832.gif" border="0" alt="C0219-02.GIF" width="108" height="28" />].</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3"><i>6.5.3<br />Forced INS Error Equations</i></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">The predominant use of sensor error models such as those described in the previous subsections is for system performance analysis. For estimator design and sensor selection the predominant method is covariance analysis. To understand the basic effects of different forms of sensor error, it is important to analyze the solution of the linearized system equations. In this section numerical solutions to the linearized system equations are presented for only the gyro bias errors.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">Figures 6.96.11 show the error state trajectory when the system is forced by constant gyro errors of 0.015掳/h. For these three figures, the system is stationary (i.e., ||v</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>e</i></sub></font><font face="Times New Roman, Times, Serif" size="3">|| = 0), level, and nominally north pointed at a latitude of 45掳 north. Therefore the eigenvalues are the same as those previously discussed. These simulations are extensions of those presented in Refs. 18 and 153.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">Figure 6.9 displays the error trajectory for the case of a 0.015掳/h uncompensated bias</font><font face="Times New Roman, Times, Serif" size="2"><sup>**</sup></font><font face="Times New Roman, Times, Serif" size="3"> in the roll (north) gyro. With reference to Eq. (6.86), the roll gyro bias causes growth of the north tilt error. The north tilt error causes east velocity and east tilt errors. The east velocity and latitude errors grow in magnitude until they cancel, on average, the roll gyro bias effects on the north tilt error. When the biased east velocity is integrated, linear growth of the longitude error results.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">Figure 6.10 displays the error trajectory for the case of a 0.015掳/h uncompensated bias in the pitch (east) gyro. The pitch gyro bias causes growth of the east tilt error. The east tilt error causes azimuth, north velocity, and north tilt error. The azimuth error develops a bias of <i>b</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>g</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3">/</font><font face="Symbol" size="3">W</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>N</i></sub></font><font face="Times New Roman, Times, Serif" size="3"> radians, which cancels the effect of the pitch bias on the east tilt error. This azimuth bias does not propagate into the remaining states since the system is stationary and the bias is perfectly canceled in the east tilt channel. Because of the azimuth error bias' canceling the pitch gyro bias, the north velocity is unbiased. Therefore the latitude error does not grow linearly with time for a stationary system. If the system were in motion, then the azimuth error would result in errors in the remaining states.</font><font face="Times New Roman, Times, Serif" size="3" color="#FFFF00"></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="24" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td> <td colspan="3" height="12"></td> <td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="24" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td></tr><tr><td colspan="3" height="1"><table cellpadding="0" cellspacing="0" border="0"><tr><td></td></tr></table></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="2"><sup>** </sup>This magnitude corresponds to one one-thousandth of the earth rate.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table></td></tr></table><p><font size="0"></font></p>聽 </td> </tr> <tr> <td align="left" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_218.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_219</strong></td> <td align="right" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_220.html">next page ></a></td> </tr> </table> </body> </html>⌨️ 快捷键说明
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